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Teoriya Veroyatnostei i ee Primeneniya, 2023, Volume 68, Issue 4, Pages 796–812
DOI: https://doi.org/10.4213/tvp5638 (Mi tvp5638) 		 
On forward and backward Kolmogorov equations for purely jump Markov processes and their generalizations

E. A. Feinberga, A. N. Shiryaevb

a Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY, USA
b Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
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DOI: https://doi.org/10.4213/tvp5638
Abstract: In the present paper, we first give a survey of the forward and backward Kolmogorov equations for pure jump Markov processes with finite and countable state spaces, and then describe relevant results for the case of Markov processes with values in standard Borel spaces based on results of W. Feller and the authors of the present paper.
Keywords: pure jump Markov process, finite and countable state spaces, standard Borel space, differentiability of the transition probability, forward and backward equations, uniqueness of the solution.
Funding agency Grant number
Russian Science Foundation 23-11-00375
SUNY - The State University of New York 231087
Received: 22.06.2023
Accepted: 30.06.2023
English version:
Theory of Probability and its Applications, 2024, Volume 68, Issue 4, Pages 643–656
DOI: https://doi.org/10.1137/S0040585X97T991684
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: E. A. Feinberg, A. N. Shiryaev, “On forward and backward Kolmogorov equations for purely jump Markov processes and their generalizations”, Teor. Veroyatnost. i Primenen., 68:4 (2023), 796–812; Theory Probab. Appl., 68:4 (2024), 643–656
Citation in format AMSBIB
\Bibitem{FeiShi23}
\by E.~A.~Feinberg, A.~N.~Shiryaev
\paper On forward and backward Kolmogorov equations for purely jump Markov processes and their generalizations
\jour Teor. Veroyatnost. i Primenen.
\yr 2023
\vol 68
\issue 4
\pages 796--812
\mathnet{http://mi.mathnet.ru/tvp5638}
\crossref{https://doi.org/10.4213/tvp5638}
\transl
\jour Theory Probab. Appl.
\yr 2024
\vol 68
\issue 4
\pages 643--656
\crossref{https://doi.org/10.1137/S0040585X97T991684}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85185273157}
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